Around 10,000 children (mostly Jewish) under threat of Nazi persecution were evacuated to the UK via Kindertransport missions. Photograph: Imagno/Getty Images

At 10 years old Ruth Jacobs took her brother by the hand and, without her parents, boarded a train in Vienna to come to England just before the outbreak of the second world war. "We had to say goodbye out of sight, they didn't want parents there on the platform," she recalled. "My parents said we would see them in a few weeks, that they would follow us. They didn't want us to worry."

Jacobs, now 84, was one of hundreds of Jewish pensioners who gathered on Sunday to honour those who helped them escape Nazi persecution, on the 75th anniversary of the establishment of the Kindertransport – the rescue mission that saved their lives.

In the final months before the war, the British parliament took the extraordinary step of accepting 10,000 children from across Europe, who traversed the continent by train and arrived by boat in British ports.

Jacobs said she would never forget the debt she owed. "I am so lucky to be here, I know that there are two million other children who are not," she said. "To my dying day, I will be forever grateful to Great Britain."

In a emotional address to the 600-strong extended Kindertransport family, the former foreign secretary David Miliband, the eldest son of Jewish immigrants, said he had "very personal reasons" to celebrate the lives and contributions of Holocaust survivors. His father and grandfather escaped to Britain in 1940, and his grandmother was sheltered by a Catholic farmer in Belgium. "As the chain of memory is broken, so history and its lessons become more important," he said. "When we ask whose responsibility is it to save lives, the answer must be: ours."

Miliband said that in taking up his new job as president of the New York-based charity International Rescue Committee, founded by the Jewish refugee Albert Einstein, he felt he was "in a small way repaying a personal debt to those who helped my parents".

Before and between the speeches the ageing kinder milled around at the Jewish Free School in north London sharing memories and fishing old photographs from handbags and pockets. As their numbers dwindled, the process of remembering the stories became more important still, said Michael Newman, chief executive of the Association of Jewish Refugees (AJR).

"This is a chance to commemorate, to tell the world this happened – but it is also a chance to say thanks to Great Britain and a reminder that we must always stand up to hatred and racism," he said.

The event was held on the 75th anniversary of a debate in Parliament which paved the way for the rescue of children from Germany, Austria, Czechoslovakia and Poland.

Some MPs argued that Jewish children could be considered "one of the best investments in the world" and would not be a burden on the state, while others feared it would bring a flood of Jewish refugees into the country.

Organised by World Jewish Relief with the backing of many supporters including the Quakers, each child had a sponsor to ensure there would be no cost to the state. Arriving by boat often at Harwich, many of them took the train to Liverpool Street station in London and went to foster families or hostels. The last group of children left Germany on 1 September 1939, the day Hitler invaded Poland.

Osias Findling, now 90, said he had come to England as a 15-year-old, leaving his parents and two younger brothers behind. "I never saw them again," he said. "They were put into a ghetto, then put on a cattle wagon and sent to the gas chambers."

He did not find out their fate until he had been in the UK for 30 years. "I myself am very grateful," he said. "This was the only country that did something, it was a wonderful gesture and that must not be forgotten."

Jacobs was more fortunate. Installed in a wealthy house on the south coast, she persuaded its mistress that her father would be a good gardener and her mother a diligent maid. "I said she was a good cook – she wasn't – and I said my father would be good in the garden, but he was a businessman," she said.

But thanks to the visas, they were able to escape. "My father said I was their luck – Mein Glück, he called me."

Judy Benton, now 92, heard about the Kindertransport after coming home to find that her parents had been taken by the Gestapo. "My neighbour said they would come back and get me too, but I said to myself I will not go to a concentration camp," she said.

Instead, at 17, she took some hidden money and her passport and made her way from Meissen, east Germany, to Leipzig where she had heard that trains were departing. But with no sponsor she had no right to board. Realising there were just a few hours before the train left, she found a fancy dress shop and bought a nurse's outfit, stowing herself on the train with no questions asked.

"My whole family died at Auschwitz," she said, sitting with her children and grandchildren. "One day you are a girl, the next you are an adult." Asked why she had attended the Kindertransport anniversary, she said: "To show I am free."

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